A burned pokémon's physical attacks will be half powered.
That explains why dragon claw did less damage. It is a physical attack, so it will only do half as much damage as before.
Some more extra effects are:
•75% less speed when paralyzed
•A Pokemon will thaw out if hit by damaging fire attacks when frozen and can still use the moves Fusion Flare, Flame Wheel, Sacred Fire, Flare Blitz and Scald when frozen
•Damage dealt from being badly poisoned will worsen over time, starting at 1/16 damage. Note that this is different from being poisoned regularly.
•Sleep does not have an extra effect, unless you count being able to use the moves Sleep Talk and Snore
Note that there are exceptions. Example: Pokemon with Quick Feet won't get speed lowered from being paralyzed.
Also, fire Pokemon cannot be burned by fire moves, ground Pokemon cannot be paralyzed by electric moves, ice Pokemon cannot be frozen by ice moves and poison Pokemon cannot be poisoned by poison moves. A Pokemon who gets poisoned and gains the steel type will remain poisoned. Usually, steel types cant be poisoned.